Find dy/dx 2x^3=2y^2+5

Problem

2*x3=2*y2+5

Solution

1. Differentiate both sides of the equation with respect to x treating y as a function of x

(d(2)*x3)/d(x)=d(2*y2+5)/d(x)

2. Apply the power rule to the left side and the chain rule to the right side.

6*x2=4*yd(y)/d(x)+0

3. Isolate the derivative term by dividing both sides of the equation by 4*y

(6*x2)/(4*y)=d(y)/d(x)

4. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2

(3*x2)/(2*y)=d(y)/d(x)

Final Answer

d(y)/d(x)=(3*x2)/(2*y)

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